Solve the inequality. Graph the solution.
6n < 90

Answer:

2060

Step-by-step explanation:

x=5*15

b=11*189

-------------

x=75

b=2079

b-x+56=2079-75+56=2060

Answer:

i just want points

Step-by-step explanation:

Answer:  4!

Step-by-step explanation:

You can turn 4 2/3 into improper fraction as 14/3. Then you have 14/3 and 6/7. You multiply both tops, then both bottoms. 6x14 is 84 and 3x7 is 21. You get 84/21 or 4. -viridiancat4, an 8th grader.

Answer: 16/7

Step-by-step explanation:

6/7 times 4 2/3 equals 16/7

Answer:

Two Column Proofs. Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. Before beginning a two column proof, start by working backwards from the "prove" or "show" statement. The reason column will typically include "given", vocabulary definitions, conjectures, and theorems.

Step-by-step explanation:

hope this helps :)

Answer:

18

Step-by-step explanation:

The lower base will 18units.

quadrilatral whose one opposite sides are parallel.

The tangent of an angle is the ratio between the opposite side of the angle and the adjacent side of the angle.

tanθ=opposite side/adjacent side

So according to asked question

in the trpezoid VWXZ,

VW || XZ

Height of trapezoid= VZ =WY=8√3

VW=10

∠YWX=30°

∠WXY=60°

In triangle ΔWYX,

∠WYX=90°

ΔWYX is a right angle triangle

so, tan∠YWX= XY/WY

⇒tan30°=XY/8√3

⇒1/√3=XY/8√3

⇒XY=8√3/√3

⇒XY=8 units

the length of the lower base ZX= ZY+XY = VW+XY = 10+8=18units

Therefore the lower base will 18units.

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Answer: 1/2

Step-by-step explanation: In this problem, we're tossing a coin and we want to find the probability of tossing a heads.

Now, let's find the probability of tossing a heads.

Remember that a coin has two sides which are heads and tails. When you flip a coin, each side is as likely to come up as the other. This means that the probability of flipping heads is the fraction 1/2.

Since the probability of flipping a heads is 1/2, we can also say that the probability of flipping a heads is 50%.

Therefore, the probability of flipping a heads on a fair coin is 1/2.

Carla bought one package each of Blue and Red pens. These are the only two packages that when combined bring the total number of pens to 49.

This problem revolves around simple arithmetic and logical reasoning. What we need to do is to figure out which combination of pen packages adds up to make 49 pens.

By looking at the numbers given, we can see that the only combination that adds up to 49 would be one package of Blue pens (25 pens) and one package of Red pens (24 pens). There is no other combination of two packages which would result in a total of 49.

Therefore, Carla would have bought one package of Blue pens and one package of Red pens to have a total of 49 pens.

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The smallest integer is 1 and middle integer is 2 and largest integer is 3

Given that , three times the largest increased by two is equal to five times the smallest increased by three times the middle integer.

We have to find the three consecutive integers

So, let the smallest integer be n, then the next two consecutive middle and largest integers will be n + 1, n + 2 respectively

Then, by the given statement,  

Three times the largest increased by two is equal to five times the smallest increased by three times the middle integer.

[tex]\begin{array}{l}{3 \times (n+2)+2=5 \times n+3 \times (n+1)} \\\\ {3 n+6+2=5 n+3 n+3} \\\\ {8=5 n+3} \\\\ {5 n=8-3} \\\\ {n=1}\end{array}[/tex]

Thus the smallest integer = n = 1

Middle integer = n + 1 = 1 + 1 = 2

Largest integer = n + 2 = 1 + 2 = 3

Final answer:

We defined three consecutive integers as x, x+1, and x+2. By setting up the equation based on the given condition and solving for x, we find that the three consecutive integers are 1, 2, and 3.

Explanation:

Let's define the three consecutive integers we are looking for as x, x+1, and x+2, where x is the smallest integer, x+1 is the middle integer, and x+2 is the largest integer.

The problem states that three times the largest increased by two is equal to five times the smallest increased by three times the middle integer. This gives us the equation:

3(x+2) + 2 = 5x + 3(x+1)

Now, simplify and solve for x:

3x + 6 + 2 = 5x + 3x + 3

6x + 8 = 8x + 3

Subtract 6x from both sides:

8 = 2x + 3

Subtract 3 from both sides to isolate the term with x:

5 = 2x

Divide both sides by 2 to solve for x:

x = 5/2 = 2.5

Since x has to be an integer, this approach shows that we've made a mistake in our calculation. Let's try again:

3x + 6 + 2 = 5x + 3x + 3

3x + 8 = 8x + 3

5 = 5x

x = 1

So the three consecutive integers are 1, 2, and 3.

Answer:

6/55 = x/44

55x = 6(44)

55x = 264

x = 264/55 = 4.8 miles

hope this helps<3

Step-by-step explanation:

Answer:

2nd graph on edge 2020

Step-by-step explanation:

the line will cross the y-axis at y = 1.5 and the line will be a broken line

Inequality graphs

The inequality functions are not separated by an equal sign.

For the inequality 4x + 2y < 3, the lower portion of the graph will be shaded

Determine the y-intercept. If x = 0

4(0) + 2y < 3
2y < 3

y < 1.5

This shows that the line will cross the y-axis at y = 1.5 and the line will be a broken line as shown:

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The value of k is -6

Step-by-step explanation:

The general form of the quadratic equation is y = ax² + bx + c

∵ 2x² + 11x = -k

- Add k to both sides

∴ 2x² + 11x + k = 0

∵ The roots of the quadratic equations is the values of x when y = 0

∵ [tex]\frac{1}{2}[/tex] is a root of the equation

- Substitute x by [tex]\frac{1}{2}[/tex] in the equation above to find k

∵ 2( [tex]\frac{1}{2}[/tex] )² + 11( [tex]\frac{1}{2}[/tex] ) + k = 0

∴ 2( [tex]\frac{1}{4}[/tex] ) + [tex]\frac{11}{2}[/tex] + k = 0

∴ [tex]\frac{1}{2}[/tex] + [tex]\frac{11}{2}[/tex] + k = 0

- Add the like terms

∵ [tex]\frac{1}{2}[/tex] + [tex]\frac{11}{2}[/tex] = [tex]\frac{12}{2}[/tex] = 6

∴ 6 + k = 0

- Subtract 6 from both sides

∴ k = -6

The value of k is -6

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Final answer:

By substituting x = 1/2 into the equation [tex]2x^2 + 11x = -k[/tex] and simplifying, we find that k must equal -6 for 1/2 to be a root of the equation.

Explanation:

To find the value of k such that 1/2 is a root of the quadratic equation [tex]2x^2 + 11x = -k[/tex], we can substitute x = 1/2 into the equation and solve for k.

First, substitute x = 1/2:

[tex]2(1/2)^2 + 11(1/2) = -k[/tex]

Then, simplify the equation:

2(1/4) + 11/2 = -k

1/2 + 11/2 = -k

Now, combine the terms:

(1 + 11)/2 = -k

12/2 = -k

6 = -k

Finally, multiply both sides by -1 to find k:

k = -6

The differential for P = 0.2x² -17x -10 is P' = 0.4x - 17

Step-by-step explanation:

Let us revise how to differentiate an equation with respect to x

If the equation is [tex]y = ax^{n}+b[/tex] , where a , b are constant

∵ P = 0.2x² - 17x - 10

- Let us differentiate each term

∵ The differentiation of 0.2x² is [tex]0.2(2)x^{2-1}=0.4x^{1}=0.4x[/tex]

∵ The differentiation of -17x is [tex]-17(1)x^{1-1}=-17x^{0}=-17(1)=-17[/tex]

∵ The differentiation of -10 is zero because the differentiation

    of the numerical term is 0

∴ The differentiation of P is P' = 0.4x - 17

The differential for P = 0.2x² -17x -10 is P' = 0.4x - 17

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Answer:

c 6 times that the answer

Final answer:

The second cube's side length is 6 times that of the first cube because the volume of a cube is a cubic function of its side length, and taking the cube root of 1/216 gives us 1/6.

Explanation:

The student's question is asking to determine how many times larger the side length of the second cube is compared to the first cube, given that the volume of the first cube is 1⁄216 times the volume of the second cube. The volume of a cube is calculated by raising the side length to the third power (V = s3). Therefore, if we denote the side length of the first cube as s and that of the second cube as S, we have s3 = 1⁄216S3. To find the side length ratio, we take the cube root on both sides of the equation, yielding s = 1⁄6S, which means the second cube's side length is 6 times that of the first cube.

The correct answer to the question is C, 6 times

The manager should sale the bookshelf for $235.20

Step-by-step explanation:

Wholesale price of book shelf = $147.00

Mark up = 60% of original price

[tex]Mark\ up=\frac{60}{100}*147.00\\\\ Mark\ up=\frac{8820}{100}\\Mark\ up=\$88.20[/tex]

Total = Wholesale price + Mark up

[tex]Total= 147.00+88.20\\Total=\$235.20[/tex]

The manager should sale the bookshelf for $235.20

Keywords: mark up, percentage

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Answer:

13.  b.  4 + 5x = 29; $5.

14.  c.  74 + w = 3w + 6; 34 pounds.

15.  b.  $42.5.

Step-by-step explanation:

13. 4 + 5x = 29

5x = 29-4 = 25

x = 5.

14. 74 + w = 3w + 6

68 = 2w

w = 34.

15. Let x be the money he got last year. Then:

2x + 5 = 90

2x = 85

x = $42.5.

Answer:

The third number line

Step-by-step explanation:

first, make each fraction a complex fraction

47/10 = 4 7/10, so you know its the 7th dash from the left.

for 4 2/5 you need to make the denominator 10 by multiplying the numerator and denominator by 2 to get 4 4/10; this should be the 4th dash.

divide 24/5 to get 4 4/5. Multiply the numerator and denominator of the fraction part to get a denominator of 10. you should get 4 8/10; this is on the 8th dash from the last

You would have a dot on the 4th 7th and 8th dash altogether

Answer:

10/31

Step-by-step explanation:

I'm pretty certain this is the answer, since 10/31 cannot be simplified any further; 31 being the total days in the month of May

A 10 days represent a fraction of approximately 0.3226 (rounded to four decimal places) of the month of May.

To find the fraction of the month that 10 days represent, we can divide the number of days represented by 10 by the total number of days in the month, which is 31.

Fraction = (Number of days represented) / (Total number of days in the month)

Fraction = 10 / 31

Therefore, 10 days represent a fraction of approximately 0.3226 (rounded to four decimal places) of the month of May.

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They must sell 18 small pizzas, 12 medium pizzas and 6 large pizzas

Step-by-step explanation:

A Pizzeria sells pizza according to size:

We need to find how many of each size pizza they must sell to get $600

Assume that the number of small pizza is x, the number of medium pizza is y and the number of large pizza is z

∵ The Pizzeria sells x small pizzas, y medium pizzas and

   z large pizzas

∵ The small pizzas cost $10, medium pizzas cost $15, and

   large pizzas cost $40

∵ They get $600

∴ 10x + 15y + 40z = 600 ⇒ (1)

∵ They sell as many small pizzas as medium and large pizzas

   combined

∴ x = y + z ⇒ (2)

∵ The number of medium pizzas sold is twice as many as large ones

∴ y = 2z ⇒ (3)

Substitute equation (3) in equation (2) to find x in terms of z only

∵ x = (2z) + z

∴ x = 3z ⇒ (4)

Substitute x in equation (1) by equation (4), and substitute y in equation (1) by equation (3)

∵ 10(3z) + 15(2z) + 40z = 600

- Simplify the left hand side

∴ 30z + 30z + 40z = 600

- Add like terms

∴ 100z = 600

- Divide both sides by 100

∴ z = 6

Substitute the value of z in equations (3) and (4) to find y and x

∵ y = 2(6)

∴ y = 12

∵ x = 3(6)

∴ x = 18

They must sell 18 small pizzas, 12 medium pizzas and 6 large pizzas

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Answer:

750:90

Step-by-step explanation:

12% of 750 is 90

Answer:

Diameter is 11.14

Step-by-step explanation:

c=dπ

so... 35=dπ

 solve for d:

      35/π=d

11.14=d

Answer:

11.14

Step-by-step explanation:

/calculators/circumference-calculator/

Answer:

154.34%

Step-by-step explanation:

We are asked to determine what percentage of 357 is 551.

Let us assume that x% of 357 is 551.

So, [tex]\frac{357 \times x}{100} = 551[/tex]

⇒ [tex]\frac{x}{100} = \frac{551}{357}[/tex]

⇒ [tex]x = \frac{551}{357} \times 100[/tex] ......... (1)

⇒ x = 154.34%

So, it is clear from the step (1) that when we take the basic ratio then multiply with 100, then we will get the percentage. (Answer)

Final answer:

To determine what percent 551 is of 357, divide 551 by 357, multiply by 100, and round to the nearest hundredth. The answer is 154.34%.

Explanation:

To find what percent 551 is of 357, we use the formula for calculating percentages: 'part over total, times one hundred, equals percent'. The 'part' in this case is 551, and the 'total' is 357.

The calculation is as follows:

Divide the part (551) by the total (357) which equals approximately 1.5434.

Multiply the result by 100 to find the percentage.

1.5434 × 100 = 154.34%

To round the final answer to the nearest hundredth, we look at the digit in the thousandths place. Since the third decimal place is 4, which is less than 5, we do not need to round up, so the rounded percentage is 154.34%.

Answer:

420 cars were tested

Step-by-step explanation:

55/100=231/x

55x= 23100

x=420

Final answer:

The total number of cars tested can be calculated by dividing the number of cars that failed (231) by the percentage that failed (55%), resulting in 420 cars tested.

Explanation:

The question asks about the total number of cars tested based on the percentage that failed the safety test. To find the total, we can set up a proportion: if 55% of cars, or 0.55 of the total, failed the safety test and that number is 231, we can represent the total number of cars tested as 'X'. Using the proportion 0.55 = 231/X, we can solve for X, which represents the total number of cars tested.

Step by step, we can start by multiplying both sides of the equation by X to get 0.55X = 231, then we divide both sides by 0.55 to isolate X and find the total:

X = 231 / 0.55
X = 420

Therefore, 420 cars were tested.

Answer:

y=4x+23

Step-by-step explanation:

The slope-intercept form of the equation of the line that passes through (-5,3) and is parallel to 12x-3y=10 is y = 4x + 23.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Slope-intercept form:

y = mx + b, where m is the slope and b is the y-intercept.

And we have the given equation:

12x - 3y = 10

Arranging the equation as slope-intercept form.

3y = 12x - 10

Divide by 3,

y = 4x - 10/3.

And this line is parallel to the required line.

So, the slope of the required line;

m = 4

Hence, the slope-intercept form,

y = 4x+b  equation 1

To find y-intercept:

We substitute the value of x and y from the point (-5,3) to the slope-intercept form,

y = 4x + b

(3) = 4(-5) + b

b = 20 +3

b = 23

Now, the equation 1

y = 4x + 23

Therefore, y = 4x + 23 is the required slope-intercept form.

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Answer:

(x - 5)(x - 7)

Step-by-step explanation:

Given

x² - 12x + 35

Consider the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (- 12)

The factors are - 5 and - 7, since

- 5 × - 7 = 35 and - 5 - 7 = - 12, thus

x² - 12x + 35 = (x - 5)(x - 7) ← in factored form

W=L+2

A=48=L*W

48=L*(L+2)

48=L^2+L*2

0=L^2+L*2-48

L1=6

L2=-8 (can't be used since it's negative)

Lenght=6

Width=8

Answer:

f(3)=7

Step-by-step explanation:

f(x)=7

f(3)=7

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{\cfrac{3}{5}}(x-\stackrel{x_1}{2})\implies y+4=\cfrac{3}{5}x-\cfrac{6}{5}[/tex]

[tex]\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y+4)=5\left( \cfrac{3}{5}x-\cfrac{6}{5} \right)}\implies 5y+20=3x-6\implies 5y=3x-26 \\\\\\ -3x+5y=-26\implies 3x-5y=26[/tex]

Answer:

x=-5, 3

Step-by-step explanation:

(x+5)(x-3)=0

Apply the zero property,

set x+5=0 and x-3=0.

x=0-5=-5

x=0+3=3

x=-5, 3

Answer:

b&e

Step-by-step explanation:

The value of x in the equation is 11/15.

To find the value of x in the equation 5 1 10 x - 6 4 5 = 3 1 4, we need to isolate x on one side of the equation. Here's how you can solve it:

Step 1: Add 645 to both sides of the equation.

Step 2: Subtract 314 from both sides of the equation.

Step 3: Simplify the equation.

Step 4: Divide both sides of the equation by 510.

Step 5: Simplify the fraction.

Therefore, the value of x in the equation is 11/15, which is option B) 11/15.

Answer:

Votes received by Billy =15

Step-by-step explanation:

Given:

Total students in the class = 20

Billy receives 3 times more vote than Keeton.

To find the number of votes Billy receives.

Solution:

Let number of votes Keeton gets [tex]=x[/tex]

∴ Billy received [tex]=3x[/tex] votes

Expression for total votes can be given by ⇒ [tex]x+3x[/tex]

Total votes =20 as number of students is 20.

So, the equation to find [tex]x[/tex] is:

[tex]x+3x=20[/tex]

Solving for  [tex]x[/tex]

⇒ [tex]4x=20[/tex]

Dividing both sides by 4.

[tex]\frac{4x}{4}=\frac{20}{4}[/tex]

∴ [tex]x=5[/tex]

∴ Votes received by Keeton = 5

Votes received by Billy = [tex]3\times 5[/tex] = 15

Answer:

6cd+10c

Step-by-step explanation:

(c+c)(3d+5)

2c(3d+5)=6cd+10c